Systems and methods for segmenting an impedance matching model are described. One of the methods includes receiving the impedance matching model. The impedance matching model represents an impedance matching circuit, which is coupled to an rf generator via an rf cable and to a plasma chamber via an rf transmission line. The method further includes segmenting the impedance matching model into two or more modules of a first set. Each module includes a series circuit and a shunt circuit. The shunt circuit is coupled to the series circuit. The series circuit of the first module is coupled to a cable model and the series circuit of the second module is coupled to an rf transmission model. The series circuit and the shunt circuit of the first module are coupled to the series circuit of the second module. The shunt circuit of the second module is coupled to the rf transmission model.
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11. A method for segmenting an impedance matching model, the method comprising:
receiving the impedance matching model, the impedance matching model representing an impedance matching circuit, the impedance matching circuit coupled to a radio frequency (rf) generator via an rf cable and to a plasma chamber via an rf transmission line;
segmenting the impedance matching model into two or more modules of a first set, each module including a series circuit and a shunt circuit, the shunt circuit coupled to the series circuit, the shunt circuit coupled to a ground connection, the series circuit of a first one of the modules coupled to a cable model, the shunt circuit of the first module coupled to the cable model, the series circuit of the first module coupled to the series circuit of the second module, the series circuit of the second module coupled to the rf transmission model, the shunt circuit of the second module coupled to the series circuit of the first module; and
replacing one of the modules of the first set with a module of a second set,
wherein the method is executed by a processor.
23. A method for segmenting an impedance matching model, the method comprising:
receiving the impedance matching model, the impedance matching model representing an impedance matching circuit, the impedance matching circuit coupled to a radio frequency (rf) generator via an rf cable and to a plasma chamber via an rf transmission line;
segmenting the impedance matching model into two or more modules of a first set, each module including a series function and a shunt function, the shunt function coupled to the series function, the shunt function coupled to a ground function, the series function of a first one of the modules coupled to a cable model, the shunt function of the first module coupled to the cable model, the series function of the first module coupled to the series function of the second module, the series function of the second module coupled to the rf transmission model, the shunt function of the second module coupled to the series function of the first module; and
replacing one of the modules of the first set with a module of a second set,
wherein the method is executed by a processor.
1. A method for segmenting an impedance matching model, the method comprising:
receiving the impedance matching model, the impedance matching model representing an impedance matching circuit, the impedance matching circuit coupled to a radio frequency (rf) generator via an rf cable and to a plasma chamber via an rf transmission line;
segmenting the impedance matching model into two or more modules of a first set, each module including a series circuit and a shunt circuit, the shunt circuit coupled to the series circuit, the shunt circuit coupled to a ground connection, the series circuit of a first one of the modules coupled to a cable model and the series circuit of a second one of the modules coupled to an rf transmission model, the series circuit of the first module coupled to the series circuit of the second module, the shunt circuit of the first module coupled to the series circuit of the second module, the shunt circuit of the second module coupled to the rf transmission model; and
replacing one of the modules of the first set with a module of a second set,
wherein the method is executed by a processor.
20. A method for segmenting an impedance matching model, the method comprising:
receiving the impedance matching model, the impedance matching model representing an impedance matching circuit, the impedance matching circuit coupled to a radio frequency (rf) generator via an rf cable and to a plasma chamber via an rf transmission line;
segmenting the impedance matching model into two or more modules of a first set, each module including a series function and a shunt function, the shunt function coupled to the series function, the shunt function coupled to a ground function, the series function of a first one of the modules coupled to a cable model and the series function of a second one of the modules coupled to an rf transmission model, the series function of the first module coupled to the series function of the second module, the shunt function of the first module coupled to the series function of the second module, the shunt function of the second module coupled to the rf transmission model; and
replacing one of the modules of the first set with a module of a second set,
wherein the method is executed by a processor.
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This application claims the benefit of and priority, under 35 U.S.C. §119(e), to U.S. Provisional Patent Application No. 61/821,523, filed on May 9, 2013, and titled “Segmenting a Model Within a Plasma System”, which is hereby incorporated by reference in its entirety
This application is a continuation-in-part (CIP) of and claims the benefit of and priority, under 35 U.S.C. §120, to U.S. patent application Ser. No. 13/756,390, filed on Jan. 31, 2013, and titled “Using Modeling to Determine Wafer Bias Associated with a Plasma System”, which is hereby incorporated by reference in its entirety.
The present embodiments relate to generating segments of a model within a plasma system.
A plasma-based system is used to perform a variety of operations. For example, the plasma-based system is used to etch a wafer, deposit materials on a wafer, clean a wafer, etc. To perform the operations, the plasma-based system includes a radio frequency (RF) generator. The RF generator is coupled to an impedance block that is further coupled to a plasma chamber.
The RF generator generates an RF signal that is transferred via the impedance block to the plasma chamber. When a gas is supplied into the plasma chamber, the gas is ignited with the RF signal and plasma is formed within the plasma chamber.
However, there may be a replacement of the impedance block with another impedance block. For example, an impedance block that is malfunctioning may be replaced with another impedance block. As another example, an impedance block that is nonoperational may be replaced with another impedance block. An impedance block may be replaced for any reason other than that the impedance block is nonoperational or malfunctioning.
It is in this context that embodiments described in the present disclosure arise.
Embodiments of the disclosure provide apparatus, methods and computer programs for generating segments of a model within a plasma system. It should be appreciated that the present embodiments can be implemented in numerous ways, e.g., a process, an apparatus, a system, a piece of hardware, or a method on a computer-readable medium. Several embodiments are described below.
In various embodiments, a model is formed from a circuit of a plasma system. For example, an impedance matching model is formed based on characteristics of an impedance matching circuit, a cable model is formed based on characteristics of a radio frequency (RF) cable, or an RF transmission model is formed based on characteristics of an RF transmission line. The model is segmented into a number of modules. Each module includes a series circuit and a shunt circuit. When a circuit of the plasma system is to be replaced with another circuit of the plasma system, one or more of the modules is easily replaced with one or more modules.
In various embodiments, a method for segmenting an impedance matching model is described. The method includes receiving the impedance matching model. The impedance matching model represents an impedance matching circuit, which is coupled to an RF generator via an RF cable and to a plasma chamber via an RF transmission line. The method further includes segmenting the impedance matching model into two or more modules of a first set. Each module including a series circuit and a shunt circuit. The shunt circuit is coupled to the series circuit. The shunt circuit is coupled to a ground connection. The series circuit of the first module is coupled to a cable model. The series circuit of the second module is coupled to an RF transmission model. The series circuit of the first module is coupled to the series circuit of the second module. The shunt circuit of the first module coupled to the series circuit of the second module. The shunt circuit of the second module is coupled to the RF transmission model. The method is executed by a processor.
In some embodiments, a method for segmenting an RF transmission model is described. The method includes receiving an RF transmission model, which represents an RF transmission line. The RF transmission line couples a plasma chamber to an impedance matching circuit, which is coupled via an RF cable to an RF generator. The method further includes segmenting the RF transmission model into two or more modules of a first set. Each module includes a series circuit and a shunt circuit. The shunt circuit is coupled to the series circuit. The shunt circuit is coupled to a ground connection and the series circuit of the first module is coupled to an impedance matching model. The series circuit of the first module coupled to the series circuit of the second module and the shunt circuit of the first module is coupled to the series circuit of the second module. The method is executed by a processor.
In a variety of embodiments, a method for segmenting a cable model is described. The method includes receiving a cable model, the cable model representing an RF cable, which couples an RF generator to an impedance matching circuit. The impedance matching circuit is coupled via an RF transmission line to a plasma chamber. The method includes segmenting the cable model into two or more modules of a first set. Each module includes a series circuit and a shunt circuit. The shunt circuit is coupled to the series circuit and to a ground connection. The series circuit of the first module receives a complex voltage and current from a voltage and current probe. The shunt circuit of the second module is coupled to an impedance matching model. The series circuit of the second module is coupled to the impedance matching model. The method is executed by a processor.
In various embodiments, a method for segmenting an impedance matching model is described. The method includes receiving the impedance matching model, which represents an impedance matching circuit. The impedance matching circuit is coupled to an RF generator via an RF cable and to a plasma chamber via an RF transmission line. The method further includes segmenting the impedance matching model into two or more modules of a first set. Each module includes a series circuit and a shunt circuit. The shunt circuit is coupled to the series circuit and to a ground connection. The series circuit of a first one of the modules is coupled to a cable model and the shunt circuit of the first module is coupled to the cable model. The series circuit of the first module is coupled to the series circuit of the second module and the series circuit of the second module coupled to the RF transmission model. The shunt circuit of the second module is coupled to the series circuit of the first module. The method is executed by a processor.
In some embodiments, a method for segmenting an impedance matching model is described. The method includes receiving the impedance matching model, which represents an impedance matching circuit. The impedance matching circuit is coupled to an RF generator via an RF cable and to a plasma chamber via an RF transmission line. The method further includes segmenting the impedance matching model into two or more modules. Each module includes a series function and a shunt function. The shunt function is coupled to the series function and to a ground function. The series function of a first one of the modules is coupled to a cable model and the series function of a second one of the modules coupled to an RF transmission model. Also, the series function of the first module is coupled to the series function of the second module and the shunt function of the first module is coupled to the series function of the second module. The shunt function of the second module is coupled to the RF transmission model. The method is executed by a processor.
In several embodiments, a method for segmenting an impedance matching model is described. The method includes receiving the impedance matching model, which represents an impedance matching circuit. The impedance matching circuit is coupled to an RF generator via an RF cable and to a plasma chamber via an RF transmission line. The method further includes segmenting the impedance matching model into two or more modules of a first set. Each module includes a series function and a shunt function. The shunt function is coupled to the series function and to a ground function. The series function of a first one of the modules is coupled to a cable model and the shunt function of the first module is coupled to the cable model. The series function of the first module is coupled to the series function of the second module and the series function of the second module is coupled to the RF transmission model. The shunt function of the second module is coupled to the series function of the first module. The method is executed by a processor.
Some advantages of the above-described embodiments include ease in replacement of one module of a model with another module of a model. For example, when an impedance matching circuit is replaced with another impedance matching circuit, one or more modules of an impedance matching model that represents the impedance matching circuit being replaced is easily switched with one or more modules of a replacement impedance matching model that represents the replacement impedance matching circuit. For example, a computer-generated code for the one or more modules of the replacement impedance matching model can be easily replaced with a computer-generated code of the one or more modules of the impedance matching model being replaced. Similarly, as another example, when an RF cable is replaced with another RF cable, one or more modules of a cable model that represents the RF cable being replaced is easily switched with one or more modules of another cable model that represents the replacement RF cable. Also, as another example, when an RF transmission line is replaced with another RF transmission line, one or more modules of an RF transmission model that represents the RF transmission line being replaced are is switched with one or more modules of another RF transmission model that represents the replacement RF transmission line.
Other aspects will become apparent from the following detailed description, taken in conjunction with the accompanying drawings.
The embodiments may best be understood by reference to the following description taken in conjunction with the accompanying drawings.
The following embodiments describe systems and methods for segmenting a model within a plasma system. It will be apparent that the present embodiments may be practiced without some or all of these specific details. In other instances, well known process operations have not been described in detail in order not to unnecessarily obscure the present embodiments.
A voltage and current (VI) probe 108 measures a complex voltage and current Vx, Ix, and φx at an output 110, of the x MHz RF generator. It should be noted that Vx represents a voltage magnitude, Ix represents a current magnitude, and φx represents a phase between Vx and Ix. Similarly, a voltage and current probe 112 measures a complex voltage and current Vy, Iy, and φy at an output 114 of the y MHz RF generator. It should be noted that Vy represents a voltage magnitude, Iy represents a current magnitude, and φy represents a phase between Vy and Iy. Moreover, a voltage and current probe 116 measures a complex voltage and current Vz, Iz, and φz at an output 118 of the z MHz RF generator. It should be noted that Vz represents a voltage magnitude, Iz represents a current magnitude, and φz represents a phase between Vz and Iz.
Examples of x MHz include 2 MHz, 27 MHz, and 60 MHz. Examples of y MHz include 2 MHz, 27 MHz, and 60 MHz. Examples of z MHz include 2 MHz, 27 MHz, and 60 MHz. The x MHz is different than y MHz and z MHz. For example, when x MHz is 2 MHz, y MHz is 27 MHz and z MHz is 60 MHz. When x MHz is 27 MHz, y MHz is 60 MHz and z MHz is 2 MHz.
An example of a voltage and current probe includes a voltage and current probe that complies with a pre-set formula. An example of the pre-set formula includes a standard that is followed by an Association, which develops standards for sensors. Another example of the pre-set formula includes a National Institute of Standards and Technology (NIST) standard. As an illustration, the voltage and current probe 108, 112, or 116 is calibrated according to NIST standard. In this illustration, the voltage and current probe 108, 112, or 116 is coupled with an open circuit, a short circuit, or a known load to calibrate the voltage and current probe to comply with the NIST standard. The voltage and current probe 108, 112, or 116 may first be coupled with the open circuit, then with the short circuit, and then with the known load to calibrate the voltage and current probe based on NIST standard. The voltage and current probe 108, 112, or 116 may be coupled to the known load, the open circuit, and the short circuit in any order to calibrate the voltage and current probe according to NIST standard. Examples of a known load include a 50 ohm load, a 100 ohm load, a 200 ohm load, a static load, a direct current (DC) load, a resistor, etc. As an illustration, each voltage and current probe 108, 112, or 116 is calibrated according NIST-traceable standards.
The voltage and current probe 108 is coupled to the output 110 of the x MHz RF generator. The output 110 is coupled to an input 120A of an impedance matching circuit 122 via an RF cable 124A. Similarly, the voltage and current probe 112 is coupled to the output 114 of the y MHz RF generator. The output 114 is coupled to another input 120B of the impedance matching circuit 122 via an RF cable 124B. Also, the voltage and current probe 116 is coupled to the output 118 of the z MHz RF generator. The output 118 is coupled to another input 120C of the impedance matching circuit 122 via an RF cable 124C.
An output 126 of the impedance matching circuit 122 is coupled to an input of an RF transmission line 128. The RF transmission line 128 is coupled to an electrostatic chuck (ESC) 132 located within a plasma chamber 130.
The impedance matching circuit 122 matches an impedance of a source coupled to the impedance matching circuit 122 with an impedance of a load coupled to the impedance matching circuit 122. For example, the impedance matching circuit 122 matches a combined impedance of the x MHz RF generator and the RF cable 124A with a combined impedance of the RF transmission line 128 and the plasma chamber 130. In this example, the x MHz RF generator is on and the y and z MHz RF generators are off.
The plasma chamber 130 includes the ESC 132, an upper electrode 134, and other parts (not shown), e.g., an upper dielectric ring surrounding the upper electrode 134, an upper electrode extension surrounding the upper dielectric ring, a lower dielectric ring surrounding a lower electrode of the ESC 132, a lower electrode extension surrounding the lower dielectric ring, an upper plasma exclusion zone (PEZ) ring, a lower PEZ ring, etc. The upper electrode 134 is located opposite to and facing the ESC 132. A work piece 136, e.g., a semiconductor wafer, a dummy wafer, etc., is supported on an upper surface 138 of the ESC 132. Various processes, e.g., chemical vapor deposition, cleaning, deposition, sputtering, etching, ion implantation, resist stripping, etc., are performed on the semiconductor wafer during production. Integrated circuits, e.g., application specific integrated circuit (ASIC), programmable logic device (PLD), etc. are developed on the semiconductor wafer and the integrated circuits are used in a variety of electronic items, e.g., cell phones, tablets, smart phones, computers, laptops, networking equipment, etc. Each of the lower electrode and the upper electrode 134 is made of a metal, e.g., aluminum, alloy of aluminum, copper, etc.
In one embodiment, the upper electrode 134 includes one or more gas inlets, e.g. holes, etc., that is coupled to a central gas feed (not shown). The central gas feed receives one or more process gases from a gas supply (not shown). Examples of a process gases include an oxygen-containing gas, such as O2. Other examples of a process gas include a fluorine-containing gas, e.g., tetrafluoromethane (CF4), sulfur hexafluoride (SF6), hexafluoroethane (C2F6), etc. The upper electrode 134 is grounded. The ESC 132 is coupled to the x, y, and z MHz RF generators via the impedance matching circuit 122.
When the process gas is supplied between the upper electrode 134 and the ESC 132 and when the x MHz RF generator, the y MHz, and/or the z MHz RF generator supplies RF signals via the impedance matching circuit 122 and the RF transmission line 128 to the ESC 132, the process gas is ignited to generate plasma within the plasma chamber 130.
When the x MHz RF generator generates and provides an RF signal via the output 110, the RF cable 124A, the impedance matching circuit 122, and the RF transmission line 128 to the ESC 132, the voltage and current probe 108 measures the complex voltage and current at the output 110. Similarly, when the y MHz generator generates and provides an RF signal via the output 114, the RF cable 124B, and the RF transmission line 128 to the ESC 132, the voltage and current probe 112 measures the complex voltage and current at the output 114. Also, when the z MHz generator generates and provides an RF signal via the output 118, the RF cable 124C, and the RF transmission line 128 to the ESC 132, the voltage and current probe 116 measures the complex voltage and current at the output 118.
The complex voltages and currents measured by the voltage and current probes 108, 112, and 116 are provided via corresponding communication devices 140A, 140B, and 140C from the corresponding voltage and current probes 108, 112, and 116 via a processor 142 of a host system 143 to a storage hardware unit (HU) 144 of the host system 143 for storage. For example, the complex voltage and current measured by the voltage and current probe 108 is provided via the communication device 140A and a cable 142A to the processor 142, the complex voltage and current measured by the voltage and current probe 112 is provided via the communication device 140B and a cable 142B to the processor 142, and the complex voltage and current measured by the voltage and current probe 116 is provided via the communication device 140C and a cable 142C to the processor 142. The processor 142 stores the complex voltages and current received from the communication devices 140A, 140B, and 140C in the storage HU 144. Examples of a communication device include an Ethernet device that converts data into Ethernet packets and converts Ethernet packets into data, an Ethernet for Control Automation Technology (EtherCAT) device, a serial interface device that transfers data in series, a parallel interface device that transfers data in parallel, a Universal Serial Bus (USB) interface device, etc.
Examples of the host system 143 include a computer, e.g., a desktop, a laptop, a tablet, etc. As used herein, the processor 142 may be a central processing unit (CPU), a microprocessor, an application specific integrated circuit (ASIC), a programmable logic device (PLD), etc. Examples of the storage HU 144 include a read-only memory (ROM), a random access memory (RAM), or a combination thereof. The storage HU 144 may be a flash memory, a redundant array of storage disks (RAID), a hard disk, etc.
The impedance matching model 102 is generated by the processor 142 and is stored within the storage HU 144. In some embodiments, the processor 142 receives the impedance matching model 102 from another processor. The impedance matching model 102 represents the impedance matching circuit 122. For example, the impedance matching model 102 has similar characteristics, e.g., capacitances, inductances, resistances, complex power, complex voltage and currents, impedance, a combination thereof, etc., as that of the impedance matching circuit 122. To illustrate, the impedance matching model 102 has the same number of capacitors, resistors, and/or inductors as that within the impedance matching circuit 122, and the capacitors, resistors, and/or inductors are connected with each other in the same manner, e.g., serial, parallel, etc. as that within the impedance matching circuit 122. In this illustration, the impedance matching model 102 has the same capacitance, or resistance, or inductance, or a combination thereof, etc., as a capacitance, or a resistance, or an inductance, or a combination thereof, etc., of the impedance matching circuit 122. To provide an illustration, when the impedance matching circuit 122 includes a capacitor coupled in series with an inductor, the impedance matching model 102 also includes a capacitor coupled in series with an inductor.
To further illustrate, the impedance matching circuit 122 includes one or more electrical components and the impedance matching model 102 includes a design, e.g., a computer-generated model, of the impedance matching circuit 122. The computer-generated model may be generated by the processor 142 based upon input signals received from a user via an input HU. The input signals include signals regarding which electrical components, e.g., capacitors, inductors, etc., to include in a model and a manner, e.g., series, parallel, etc., of coupling the electrical components with each other. To illustrate, the impedance circuit 122 includes hardware electrical components and hardware connections between the electrical components and the impedance matching model 102 includes software representations of the hardware electrical components and of the hardware connections. To provide yet another illustration, the impedance matching model 102 is designed using a software program and the impedance matching circuit 122 is made on a printed circuit board. As used herein, electrical components may include resistors, capacitors, inductors, connections between the resistors, connections between the inductors, connections between the capacitors, and/or connections between a combination of the resistors, inductors, and capacitors.
To provide another illustration, the impedance matching model 102 is represented by a function as that used to represent the impedance matching circuit 122. For example, the impedance matching model 102 is represented by a function, e.g., a mathematical function, etc., of resistances and reactances, and the function represents the impedance matching circuit 122.
The cable models 104A, 104B, 104C, and the RF transmission model 106 are generated by the processor 142 and are stored in the storage HU 144. In some embodiments, the cable models 104A, 104B, 104C, and the RF transmission model 106 are received by the processor 142 from another processor.
The cable model 104A represents the RF cable 124A, the cable model 104B represents the RF cable 124B, and the cable model 104C represents the RF cable 124C. For example, the cable model 104A and the RF cable 124A has similar characteristics, a cable model 104B and the RF cable 124B has similar characteristics, and a cable model 104C and the RF cable 124C has similar characteristics. For example, the cable model 104B has the same number of circuit elements, e.g., resistors, capacitors and/or inductors, etc., as that within the RF cable 124A, and the resistors, capacitors and/or inductors are connected with each other in the same manner, e.g., serial, parallel, etc. as that within the RF cable 124A. As another example, an inductance, a capacitance, or a combination thereof, etc., of the cable model 104A is the same as an inductance, a capacitance, or a combination thereof, etc., of the RF cable 124A. As another example, the cable model 104A is a computer-generated model of RF cable 124A, the cable model 104B is a computer-generated model of the RF cable 124B, and the cable model 104C is a computer-generated model of the RF cable 124C. As yet another example, the cable model 104A is represented by a function, e.g., a mathematical function, etc., of resistances and reactances, and the function represents the RF cable 124A. As another example, the cable model 104B is represented by a function, e.g., a mathematical function, etc., of resistances and reactances, and the function represents the RF cable 124B. As another example, the cable model 104C is represented by a function, e.g., a mathematical function, etc., of resistances and reactances, and the function represents the RF cable 124C. The cable model 104A has an input 105A, the cable model 104B has an input 105B, and the cable model 104C has an input 105C.
The RF transmission model 106 represents the RF transmission line 128. For example, the RF transmission model 106 and the RF transmission line 128 have similar characteristics. As another example, the RF transmission model 106 has the same number of circuit elements, e.g., resistors, capacitors and/or inductors, etc., as that within the RF transmission line 128, and the resistors, capacitors and/or inductors are connected with each other in the same manner, e.g., serial, parallel, etc. as that within the RF transmission line 128. To further illustrate, when the RF transmission line 128 includes a capacitor coupled in parallel with a resistor, the RF transmission model 106 also includes the capacitor coupled in parallel with the resistor. As yet another example, the RF transmission line 128 includes one or more electrical components and the RF transmission model 106 includes a design, e.g., a computer-generated model, of the RF transmission line 128. As another example, the RF transmission model 106 is represented by a function, e.g., a mathematical function, etc., of resistances and reactances, and the function represents the RF transmission line 128. As another example, an impedance, an inductance, a capacitance, or a combination thereof, etc., of the RF transmission model 106 is the same as an impedance, inductance, a capacitance, or a combination thereof, etc., of the RF transmission line 128.
In some embodiments, the RF transmission model 106 is a computer-generated impedance transformation involving computation of characteristics, e.g., capacitances, resistances, inductances, a combination thereof, etc., of elements, e.g., capacitors, inductors, resistors, a combination thereof, etc., and determination of connections, e.g., series, parallel, etc., between the elements.
The processor 142 generates the impedance matching model 102 and converts, e.g., segments, etc., the impedance matching model 102 into one or more modules. Similarly, the processor 142 generates the cable model 104A and converts, segments, etc., the cable model 104A into one or more modules, generates the cable model 104B and converts the cable model 104B into one or more modules, and generates the cable model 104C and segments the cable model 104C into one or more modules. Moreover, the processor 142 generates the RF transmission model 106 and converts, segments, etc., the RF transmission model 106 into one or more modules.
Based on the complex voltage and current received at the input 105A from the voltage and current probe 108 via the cable 142A and characteristics, e.g., impedance, resistance, reactance, complex voltage and current, etc., of the one or more modules of the cable model 104A, the processor 142 calculates a complex voltage and current at an input 146A of the impedance matching model 102. The complex voltage and current at the input 146A is stored in the storage HU 144.
Similarly, based on the complex voltage and current received at the input 105B from the voltage and current probe 112 via the cable 142B and characteristics, e.g., impedance, resistance, reactance, complex voltage and current, etc., of the one or more modules of the cable model 104B, the processor 142 calculates a complex voltage and current at an input 146B of the impedance matching model 102. Also, based on the complex voltage and current received at the input 105C from the voltage and current probe 116 via the cable 142C and characteristics, e.g., impedance, resistance, reactance, complex voltage and current, etc., of the one or more modules of the cable model 104C, the processor 142 calculates a complex voltage and current at an input 146C of the impedance matching model 102.
Moreover, based on the complex voltage and current at the input 146A and characteristics, e.g., impedance, resistance, reactance, complex voltage and current, etc., of the one or more modules of the impedance matching model 102, the processor 142 calculates a complex voltage and current at an output 148 of the impedance matching model 102. A complex voltage and current at the output 148 is stored in the storage HU 144.
Similarly, based on the complex voltage and current at the input 146B and characteristics, e.g., impedance, resistance, reactance, complex voltage and current, etc., of the one or more modules of the impedance matching model 102, the processor 142 calculates a complex voltage and current at the output 148 of the impedance matching model 102. Also, based on the complex voltage and current at the input 146C and characteristics, e.g., impedance, resistance, reactance, complex voltage and current, etc., of the one or more modules of the impedance matching model 102, the processor 142 calculates a complex voltage and current at the output 148 of the impedance matching model 102.
In some embodiments, a voltage magnitude is a root mean square (RMS) voltage and a current magnitude is an RMS current.
The output 148 is coupled to an input of the RF transmission model 106, which is stored in the storage HU 144.
Based on the complex voltage and current at the output 148 and characteristics, e.g., impedance, resistance, reactance, complex voltage and current, etc., of the one or more modules of the RF transmission model 106, the processor 142 calculates a complex voltage and current at an output 150 of the RF transmission model 106. The output 150 is a model of an output 151 of the RF transmission line 128 and the output 151 is coupled to the ESC 132 to provide RF signals generated by one or more of the x, y, and z MHz RF generators to the ESC 132. The complex voltage and current determined at the output 150 is stored in the storage HU 144.
It should be noted that although three generators are shown coupled to the impedance matching circuit 122, in one embodiment, any number of RF generators, e.g., a single generator, two generators, etc., are coupled to the plasma chamber 130 via an impedance matching circuit.
It should further be noted that although the above embodiments are described with respect to using a complex voltage and current, instead of the complex voltage and current, the embodiments may be described using impedances. For example, based on an impedance determined from the complex voltage and current received from the voltage and current probe 108 via the cable 142A and the one or more modules of the cable model 104A, the processor 142 calculates an impedance at the input 146A of the impedance matching model 102. The impedance is determined by the processor 142 from the complex voltage and current received from the voltage and current probe 108. As another example, based on the impedance at the input 146A and the one or more modules of the impedance matching model 102, the processor 142 calculates an impedance at the output 148 of the impedance matching model 102. As yet another example, based on the impedance at the output 148 and the one or more modules of the RF transmission model 106, the processor 142 calculates an impedance at the output 150 of the RF transmission model 106.
The processor 142 maintains a coupling between elements of the impedance matching model 102 after the segmentation of the impedance matching model 102 into modules 201, 203, and 205. For example, the processor maintains a series connection or a parallel connection between two circuit elements, e.g., a capacitor and an inductor, a resistor and an inductor, a capacitor and a resistor, etc., of the impedance matching model 102 before and after the segmentation.
The modules 201, 203, and 205 of the impedance matching model 103 are coupled with each other. For example, the module 201 is coupled to the module 203 via a link 202 and the module 203 is coupled to the module 205 via a link 204.
The module 201 has an input 206, which is an example of the input 146A, the input 146B, or the input 146C (
To generate an impedance matching model of another impedance matching circuit (not shown), e.g., a circuit that is other than and that replaces the impedance matching circuit 122 (
A series combination of the replacement modules (not shown) that replaces the corresponding modules 201, 203, and/or 205 has similar characteristics as that of the other impedance matching circuit (not shown). For example, a combined impedance of the replacement modules (not shown) is the same as or within a range of an impedance of the other impedance matching circuit (not shown). In this example, the replacement modules (not shown) represent the other impedance matching circuit (not shown). As another example, a combined impedance of one of the replacement modules (not shown), the module 203, and the module 205 is the same as or within a range of an impedance of the other impedance matching circuit (not shown). In this example, the one of the replacement modules (not shown), the module 203, and the module 205 represent the other impedance matching circuit (not shown). Modularity of impedance matching models allows easy replacement of one or more modules of one of the impedance matching models with one or more modules of another one of the impedance matching models.
Upon replacing the module 201 with another module (not shown), replacing the module 203 with another module (not shown), and/or replacing the module 205 with another module, the processor 142 checks whether characteristics, e.g., impedance, complex voltage and current, etc., of an impedance matching model that includes one or more of the replacement modules (not shown) and/or one or more of the modules 201, 203, and 205 are similar to characteristics, e.g., impedance, complex voltage and current, etc., of the other impedance matching circuit (not shown). For example, the processor 142 calculates a combined impedance of the replacement modules (not shown) and/or one or more of the modules 201, 203, and 205 and compares the combined impedance with an impedance of the other replacement impedance matching circuit (not shown). Upon determining that the combined impedance of the replacement modules (not shown) and/or one or more of the modules 201, 203, and 205 matches with or is within a range of the impedance of the other replacement impedance matching circuit (not shown), the processor 142 determines that characteristics of the impedance matching model that includes one or more of the replacement modules (not shown) and/or one or more of the modules 201, 203, and 205 are similar to characteristics of the other impedance matching circuit (not shown). On the other hand, upon determining that the combined impedance of the replacement modules (not shown) and/or one or more of the modules 201, 203, and 205 do not match with or is not within a range of the impedance of the other replacement impedance matching circuit (not shown), the processor 142 determines that characteristics of the impedance matching model that includes one or more of the replacement modules (not shown) and/or one or more of the modules 201, 203, and 205 are not similar to characteristics of the other impedance matching circuit (not shown).
In various embodiments, the impedance of the other replacement impedance matching circuit is received by the processor 142 from another processor. In some embodiments, the impedance of the other replacement impedance matching circuit is calculated by the processor 142 based on complex voltages and currents measured at an input and at an output of the other replacement impedance matching circuit.
The module n has an input 224, which is an example of the input 206, the input 210, or the input 214 (
As shown, the series circuit 218 is coupled to the input 224 and to the output 226. Moreover, the shunt circuit 220 is coupled to the output 226.
In some embodiments, a quadratic function is used instead of the series circuit 218 and a quadratic function is used instead of the shunt circuit 220. The quadratic function that is used instead of the series circuit 218 represents a directional sum of resistances of all elements of the series circuit 218 and a directional sum of reactances of the elements of the series circuit. For example, the series circuit is represented as Rs+jXs, where Rs is a result of a directional sum of resistances of all elements of the series circuit 218, Xs is a result of a directional sum of reactances of all elements of the series circuit 218, and j is the imaginary unit. Moreover, the quadratic function that is used instead of the shunt circuit 220 represents a directional sum of resistances of all elements of the shunt circuit 220 and a directional sum of reactances of all elements of the shunt circuit 220. For example, the shunt circuit is represented as Rp+jXp, where Rp is a result of a directional sum of resistances of all elements of the shunt circuit 220, and Xp is a result of a directional sum of reactances of all elements of the shunt circuit 220.
In various embodiments, the series circuit 218 or the shunt circuit 220 includes a resistor coupled in series with an inductor and a capacitor. In some embodiments, the series circuit 218 or the shunt circuit 220 includes a resistor coupled in series with an inductor or in series with a capacitor. In several embodiments, the series circuit 218 or the shunt circuit 220 includes an inductor coupled in series with a capacitor. In several embodiments, the series circuit 218 or the shunt circuit 220 includes an inductor, a resistor, or a capacitor.
In some embodiments, the processor 142 (
In several embodiments, when the nth module is a first module of the impedance matching model 103, the processor 142 determines the impedance Zn−in at an input of the nth module based on an impedance at the output 110 (
In some embodiments, an impedance at an output of an RF generator is a load impedance as seen by the generator. For example, an impedance at the output 110 of the x MHz RF generator is a load impedance as seen by the x MHz RF generator.
In various embodiments, the processor 142 (
In some embodiments, the power Pn−in input to the nth module is determined based on the complex voltage and current measured at the output 110 (
When there are N modules in the impedance matching model 103, the processor 142 determines a current In−out, e.g., root mean square current, current magnitude, etc., at an output of the nth module based on the power Pn−in and the impedance Zn−in of the nth module. For example, the processor 142 determines the current In−out as a square root of a ratio of the power Pn−in and a resistance of the impedance Zn−in. Moreover, when there are N modules in the impedance matching model 103, the processor 142 determines a voltage Vn−out, e.g., root mean square voltage, voltage magnitude, etc., at an output of the nth module based on the current In−out and the impedance Zn−in. For example, the processor 142 calculates the voltage Vn−out as a product of the current In−out and a magnitude of the impedance Zn−in.
The series RLC circuit 232 includes a resistor Rfs, an inductor Lfs, and a capacitor Cfs. The resistor Rfs is coupled in series with the inductor Lfs, and the inductor Lfs is coupled in series with the capacitor Cfs. The parallel RLC circuit 234 includes a resistor Rfp, an inductor Lfp, and a capacitor Cfp. The resistor Rfp is coupled in series with the inductor Lfp, and the inductor Lfp is coupled in series with the capacitor Cfp. The capacitor Cfp is coupled to a ground connection 236.
Inductances of the inductor Lfs and Lfp are fixed, e.g., constant. Similarly, capacitances of the capacitors Cfs and Cfp are fixed. Also, resistances of the resistors Rfs and Rfp are fixed.
In some embodiments, a value of resistance of the resistor Rfs is zero and/or a value of resistance of the resistor Rfp is zero. In various embodiments, a value of inductance of the inductor Lfs is zero, a value of inductance of the inductor Lvs is zero, a value of inductance of the inductor Lfp is zero, and/or a value of inductance of the inductor Lvp is zero. In some embodiments, a value of capacitance of the capacitor Cfs is zero, a value of capacitance of the capacitor Cvs is zero, a value of capacitance of the capacitor Cfp is zero, and/or a value of capacitance of the capacitor Cvp is zero.
The processor 142 (
Rs=As0+As1(F−F0)+As2(F−F0)2 (3)
The processor 142 calculates the reactance Xs based on the center frequency of the x MHz RF generator, based on the actual frequency of the x MHz RF generator, and based on one or more coefficients. For example, the processor 142 calculates the reactance Xs as a function:
Xs=Bs0+Bs1(F−F0)+Bs2(F−F0)2 (4)
The processor 142 calculates the resistance Rp based on the center frequency of the x MHz RF generator, based on the actual frequency of the x MHz RF generator, and based on one or more coefficients. For example, the processor 142 calculates the resistance Rp as a function:
Rp=Ap0+Ap1(F−F0)+Ap2(F−F0)2 (5)
The processor 142 calculates the reactance Xp based on the center frequency of the x MHz RF generator, based on the actual frequency of the x MHz RF generator, and based on one or more coefficients. For example, the processor 142 calculates the reactance Xp as a function:
Xp=Bp0+Bp1(F−F0)+Bp2(F−F0)2 (6)
In some embodiments, the processor 142 determines impedances, e.g., resistances, reactances, etc., at a point within the impedance matching circuit 122 (
In some embodiments, an impedance of a circuit element of a model is equal to a resistance of the circuit element when a reactance of the circuit element is zero. In various embodiments, an impedance of a circuit element of a model is equal to a reactance of the circuit element when a resistance of the circuit element is zero.
In the embodiments described with reference to
In some embodiments, the x MHz model 302 receives a complex voltage and current from the probe 108 (
In several embodiments, the x MHz matching model 302 includes any number of inductors, any number of capacitors, and/or any number of resistors. In some embodiments, the y MHz matching model 306 includes any number of inductors, any number of capacitors, and/or any number of resistors. In several embodiments, the z MHz matching model 308 includes any number of inductors, any number of capacitors, and/or any number of resistors. For example, the circuit 300 may be changed to include resistive losses in one or more of the capacitors C1, C2, C3, C4, C5, C6, C7, and C8. As another example, the circuit 300 may be changed to include resistive losses in one or more of the inductors L1, L2, L3, L4, L5, L6, and L7. As yet another example, the circuit 300 may be changed to include variable inductance of one or more of the capacitors C1, C2, C3, C4, C5, C6, C7, and C8. As another example, the circuit 300 may be changed to include variable capacitance of one or more of the inductors L1, L2, L3, L4, L5, L6, and L7. As another example, the circuit 300 may be changed to include a stray capacitance to a ground connection. As yet another example, the circuit 300 may be changed to include a capacitance and/or an inductance of an RF strap of the RF transmission line 128. As another example, the circuit 300 may be changed to consider finite length of one or more of the inductors L1, L2, L3, L4, L5, L6, and L7 and the finite length is not negligible compared to a wavelength of an RF signal that transfers through the inductor.
The module 402 includes the inductor L5, which is a shunt circuit that acts a shunt to a series circuit 410. Moreover, the module 404 includes the capacitor C6. The series circuit 410 and the inductor L5 are coupled to an output 414 of the module 402. The series circuit 412 and the capacitor C6 are coupled to an output 415 of the module 404. The series circuit 412 is also coupled to the output 414 of the module 402.
The module 406 includes a series circuit 416 that includes the capacitor C7 and the inductor L6. The inductor L6 is coupled in series to the capacitor C7. Moreover, the module 406 includes the capacitor C8. The series circuit 416 and the capacitor C8 are coupled to an output 417 of the module 406. The series circuit 416 is also coupled to the output 415 of the module 404.
Also, the module 408 includes a series circuit 418 that includes the inductor L7. The module 408 includes a shunt circuit 420 that includes the inductors L1, L2, L3, L4, and the capacitors C1, C2, C3, C4, and C5. The circuit 420 acts as shunt to the series circuit 418. The series circuit 418 is coupled to the output 417 of the module 406. Also, the series circuit 418 and the shunt circuit 420 are coupled to an output 419, which is an example of the output 216 (
In some embodiments, a combined capacitance of two capacitors in parallel with each other having positively charged plates coupled to an input wire and negatively charged plates coupled to an output wire is a sum of capacitances of the two capacitors. In various embodiments, a combined capacitance of two capacitors in series with each other having a positively charged plate of a first one of the two capacitors coupled to a negatively charged plate of a second one of the two capacitors is equal to a ratio of a product of capacitances of the two capacitors to a sum of the two capacitances.
In various embodiments, a combined inductance of two inductors in series with each other having a positively charged terminal of a first one of the two inductors coupled to a negatively charged terminal of a second one of the two inductors is equal to a sum of inductances of the two inductors. In various embodiments, a combined inductance of two inductors in parallel with each other having a positively charged terminal of a first one of the two inductors coupled to a negatively charged terminal of a second one of the two inductors is equal to a ratio of product of inductances of the two inductors to a sum of the inductances of the two inductors.
In several embodiments, a combined resistance of two resistors in series with each other having a positively charged terminal of a first one of the two resistors coupled to a negatively charged terminal of a second one of the two resistors is equal to a sum of resistances of the two resistors. In various embodiments, a combined resistance of two resistors in parallel with each other having a positively charged terminal coupled to a first end of the two resistors and having a negatively charged terminal coupled to a second end of the two resistors is equal to a ratio of product of resistances of the two resistors to a sum of resistances of the two resistors.
In various embodiments, a combined impedance of an inductor and a capacitor in series with each other is a sum of an impedance of the inductor and an impedance of the capacitor. In some embodiments, a combined impedance of a resistor and a capacitor in series with each other is a sum of an impedance of the resistor and an impedance of the capacitor. In a number of embodiments, a combined impedance of a resistor and an inductor in series with each other is a sum of an impedance of the resistor and an impedance of the inductor.
In some embodiments, a combined impedance of an inductor and a capacitor in parallel with each other is a ratio of a product of an impedance of the inductor and an impedance of the capacitor over a sum of the impedance of the inductor and the impedance of the capacitor. In various embodiments, a combined impedance of an inductor and a resistor in parallel with each other is a ratio of a product of an impedance of the inductor and an impedance of the resistor over a sum of the impedance of the inductor and the impedance of the resistor. In several embodiments, a combined impedance of an inductor and a capacitor in parallel with each other is a ratio of a product of an impedance of the inductor and an impedance of the capacitor over a sum of the impedance of the inductor and the impedance of the capacitor.
In various embodiments, the module 502 represents an effect of the x and y MHz matching models 302 and 306 (
The module 229 is an example of any of the modules N of the impedance matching model 103 (
In some embodiments, the module 229 includes only one series circuit 218 and only one shunt circuit 220.
In the embodiments described with reference to
It should be noted that the cable model generated by converting the cable model 104A may have different number of modules than that of the cable model generated by converting the cable model 104B and that of the cable model generated by converting the cable model 104C. Similarly, the cable model generated by converting the cable model 104B may have different number of modules than that of the cable model cable model generated by converting the cable model 104C. Moreover, it should be noted that the RF transmission model 106 may have a different number of modules than that of the cable model generated by converting the cable model 104A, or the cable model generated by converting the cable model 104B, or the cable model generated by converting the cable model 104C. The cable model/RF transmission model 600 includes one or more modules, e.g., a module 602, a module 604, and a module 606.
In some embodiments, the RF transmission model 600 is generated by converting, e.g., segmenting, etc., the RF transmission model 106, which is a circuit that includes one or more resistors, or one or more capacitors, or one or more inductors, or a combination thereof. In the circuit that includes one or more resistors, or one or more capacitors, or one or more inductors, or a combination thereof, in some embodiments, a capacitor is coupled in series or in parallel to another capacitor, a resistor, or an inductor. In the circuit that includes one or more resistors, or one or more capacitors, or one or more inductors, or a combination thereof, in various embodiments, a resistor is coupled in series or in parallel to another resistor, a capacitor, or an inductor. In the circuit that includes one or more resistors, or one or more capacitors, or one or more inductors, or a combination thereof, in several embodiments, an inductor is coupled in series or in parallel to another inductor, a capacitor, or a resistor.
Similarly, in various embodiments, the cable model 600 is generated by converting, e.g., segmenting, etc., the cable model 104A, 104B, or 104C (
The processor 142 (
Similarly, in various embodiments, the processor 142 (
The processor 142 maintains a coupling between elements of a cable model/RF transmission model after the segmentation of the cable model/RF transmission model into modules 602, 604, and 606. For example, the processor maintains a series connection or a parallel connection between two elements, e.g., a capacitor and an inductor, a resistor and an inductor, a capacitor and a resistor, etc., of the RF transmission model 106 before and after the segmentation. As another example, the processor maintains a series connection or a parallel connection between two elements, e.g., a capacitor and an inductor, a resistor and an inductor, a capacitor and a resistor, etc., of the cable model 104A before and after the segmentation.
The modules 602, 604, and 606 are coupled with each other. For example, the module 602 is coupled to the module 604 via a link 608 and the module 606 is coupled to the module 604 via a link 610.
In embodiments in which the cable model 600 is generated by converting the cable model 104A, 104B, or 104C, the module 602 has an input 612, which is an example of the input 105A, the input 105B, or the input 105C (
It should be noted that in various embodiments, when an output of a cable model is coupled to an input of the impedance matching model 102, the output is represented by the input and vice versa. For example, an output of the cable model 104A is represented by the input 146A, an output of the cable model 104B is represented by the input 146B, and an output of the cable model 104C is represented by the input 146C.
In embodiments in which the RF transmission model 600 is generated by converting the RF transmission model 106 (
In various embodiments, the cable model/RF transmission model 600 includes modules 602, 604, and 606 per unit length of an RF cable, e.g., the RF cable 124A, or the RF cable 124B, or the RF cable 124C, etc., or per unit length of the RF transmission line 128 (
In some embodiments, the processor 142 determines the unit length of an RF cable or an RF transmission line to be less than a fraction of a wavelength of an RF signal that is transferred via the RF cable or the RF transmission line. For example, the unit length is less than 0.1 of a wavelength of an RF signal that is transferred via the RF cable or the RF transmission line. As another example, the unit length is less than a fraction of a wavelength of an RF signal that is transferred via the RF cable or the RF transmission line, where the fraction ranges from 0.1 to 0.2.
The module d/e has an input 706, which is an example of the input 612, the input 616, or the input 620 (
As shown, the series circuit 702 is coupled to the input 706 and to the output 708. Moreover, the shunt circuit 704 is coupled to the output 708.
In various embodiments, the series circuit 702 or the shunt circuit 704 includes a resistor coupled in series with an inductor and a capacitor. In some embodiments, the series circuit 702 or the shunt circuit 704 includes a resistor coupled in series with an inductor or in series with a capacitor. In several embodiments, the series circuit 702 or the shunt circuit 704 includes an inductor coupled in series with a capacitor. In several embodiments, the series circuit 702 or the shunt circuit 704 includes an inductor, a resistor, or a capacitor.
In some embodiments, an impedance function is used instead of the series circuit 702 and an impedance function is used instead of the shunt circuit 704. The impedance function that is used instead of the series circuit 702 represents a directional sum of impedances of all elements of the series circuit 702. For example, the series circuit 702 is represented as Rsx+jXsx, where Rsx is a result of a directional sum of resistances of all elements of the series circuit 702, and Xsx is a result of a directional sum of reactances of all elements of the series circuit 702. Moreover, the impedance function that is used instead of the shunt circuit 704 represents a directional sum of resistances of all elements of the shunt circuit 704 and a directional sum of reactances of all elements of the shunt circuit 704. For example, the shunt circuit 704 is represented as Rpx+jXpx, where Rpx is a result of a directional sum of resistances of all elements of the shunt circuit 704, and Xpx is a result of a directional sum of reactances of all elements of the shunt circuit 704.
In some embodiments, the processor 142 (
In some embodiments, the processor 142 calculates the impedance Zf−in at the input 612 (
In various embodiments, the processor 142 calculates the impedance Zf−in at the input 612 (
To generate a cable model/RF transmission model of another RF cable/RF transmission line (not shown), e.g., a circuit that replaces and is other than that of RF cable 124A, or a circuit that replaces and is other than that of RF cable 124B, or a circuit that replaces and is other than that of RF cable 124C, or a circuit that replaces and is other than that of RF transmission line 128 (
A series combination of the other modules (not shown) that replaces the corresponding modules 602, 604, and/or 606 has similar characteristics as that of the other replacement RF cable/RF transmission line (not shown). For example, a combined impedance of the other modules (not shown) is the same as or within a range of an impedance of the other RF cable/RF transmission line (not shown). In this example, the other modules (not shown) represent the other RF cable/RF transmission line (not shown). As another example, a combined impedance of one of the other replacement modules (not shown), the module 604, and the module 606 is the same as or within a range of an impedance of the other RF cable/RF transmission line (not shown). In this example, the one of the other replacement modules (not shown), the module 604, and the module 606 represent the other RF cable/RF transmission line (not shown). Modularity of RF cable/RF transmission lines allows easy replacement of one or more modules of one of the RF cable/RF transmission lines with one or more modules of another one of the RF cable/RF transmission lines.
Upon replacing the module 602 with another module (not shown), replacing the module 604 with another module (not shown), and/or replacing the module 606 with another module, the processor 142 checks whether characteristics, e.g., impedance, complex voltage and current, etc., of a cable model/RF transmission model that includes one or more of the replacement modules (not shown) and/or one or more of the modules 602, 604, and 606 are similar to characteristics, e.g., impedance, complex voltage and current, etc., of the other RF cable/RF transmission line (not shown). For example, the processor 142 calculates a combined impedance of the replacement modules (not shown) and/or one or more of the modules 602, 604, and 606 and compares the combined impedance with an impedance of the other replacement RF cable/RF transmission line (not shown). Upon determining that the combined impedance of the replacement modules (not shown) and/or one or more of the modules 602, 604, and 606 matches with or is within a range of the impedance of the other replacement RF cable/RF transmission line (not shown), the processor 142 determines that characteristics of the cable model/RF transmission model that includes one or more of the replacement modules (not shown) and/or one or more of the modules 602, 604, and 606 are similar to characteristics of the other RF cable/RF transmission line (not shown). On the other hand, upon determining that the combined impedance of the replacement modules (not shown) and/or one or more of the modules 602, 604, and 606 do not match with or are not within a range of the impedance of the other replacement RF cable/RF transmission line (not shown), the processor 142 determines that characteristics of the cable model/RF transmission model that includes one or more of the replacement modules (not shown) and/or one or more of the modules 602, 604, and 606 are not similar to characteristics of the other RF cable/RF transmission line (not shown).
In various embodiments, the impedance of the other replacement RF cable/RF transmission line is received by the processor 142 from another processor. In some embodiments, the impedance of the other replacement RF cable/RF transmission line is calculated by the processor 142 based on complex voltages and currents measured at an input and at an output of the other replacement RF cable/RF transmission line.
In some embodiments, the series circuit 702 is placed to the right of the shunt circuit 704. For example, the series circuit 702 is coupled to the input 706, the shunt circuit 704, and to the output 708. Moreover, the shunt circuit 704 is coupled to the input 706 and to the ground connection 706. As another example, the shunt circuit 704 shunts a signal that is received as an input by the series circuit 702. Comparatively, the shunt circuit 704 of the module d/e shunts a signal that is provided as an output by the series circuit 702. These embodiments are similar to the embodiments of the module 229 illustrated with respect to
The series inductor circuit 804 includes an inductor Lcs. The parallel capacitor circuit 806 includes a capacitor Ccp. The capacitor Ccp is coupled to a ground connection 808.
Values of the inductor Lcs and the capacitor Ccp are fixed.
In some embodiments, a value of inductance of the inductor Lcs is zero and/or a value of capacitance of the Ccp is zero. In various embodiments, a value of inductance of the inductor Lms is zero and/or a value of capacitance of the Cmp is zero.
In the embodiments described with reference to
When one of the x, y, and z MHz RF generators is on, e.g., powered on, etc., and the remaining of the x, y, and z MHz RF generators are off, the processor 142 applies a projected complex voltage and current determined at the output 150 (
Moreover, when two of the x, y, and z MHz RF generators are on and the remaining of the x, y, and z MHz RF generators are off, the processor 142 calculates a wafer bias at the output 150 as a sum of a first product a12*V1, a second product b12*I1, a third product c12*sqrt(P1), a fourth product d12*V2, a fifth product e12*I2, a sixth product f12*sqrt(P2), and a constant g12, where V1 is a voltage magnitude at the output 150 as a result of a first one of the two RF generators being on, I1 is a current magnitude at the output 150 as a result of the first RF generator being on, P1 is a power magnitude at the output 150 as a result of the first RF generator being on, V2 is a voltage magnitude at the output 150 as a result of a second one of the two RF generators being on, I2 is a current magnitude at the output 150 as a result of the second RF generator being on, and P2 is a power magnitude at the output 150 as a result of the second RF generator being on, a12, b12, c12, d12, e12, and f12 are coefficients, and g12 is a constant.
As yet another example, when all of the x, y, and z MHz RF generators are on, the processor 142 calculates a wafer bias at the output 150 as a sum of a first product a123*V1, a second product b123*I1, a third product c123*sqrt(P1), a fourth product d123*V2, a fifth product e123*I2, a sixth product f123*sqrt(P2), a seventh product g123*V3, an eighth product h123*I3, a ninth product i123*sqrt(P3), and a constant j123, where V1, I1, P1, V2, I2, and P2 are described above in the preceding example, V3 is a voltage magnitude at the output 150 as a result of a third one of the RF generators being on, I3 is a current magnitude at the output 150 as a result of the third RF generator being on, and P3 is a power magnitude at the output 150 as a result of the third RF generator being on, a123, b123, c123, d123, e123, f123, g123, h123, and i123 are coefficients and j123 is a constant.
In some embodiments, a function used to determine a wafer bias is a sum of characterized values and a constant. The characterized values include magnitudes, e.g., the magnitudes V, I, P, V1, I1, P1, V2, I2, P2, V3, I3, P3, etc. The characterized values also include coefficients, e.g., the coefficients, a1, b1, c1, a12, b12, c12, d12, e12, f12, a123, b123, c123, d123, e123, f123, g123, h123, i123, etc. Examples of the constant include the constant d1, the constant g12, the constant j123, etc.
It should be noted that the coefficients of the characterized values and the constant of the characterized values incorporate empirical modeling data. For example, wafer bias is measured for multiple times within the plasma chamber 130 (
In some embodiments, a function used to determine a wafer bias is a polynomial.
It is noted that although the above-described operations are described with reference to a parallel plate plasma chamber, e.g., a capacitively coupled plasma chamber, etc., in some embodiments, the above-described operations apply to other types of plasma chambers, e.g., a plasma chamber including an inductively coupled plasma (ICP) reactor, a transformer coupled plasma (TCP) reactor, conductor tools, dielectric tools, a plasma chamber including an electron-cyclotron resonance (ECR) reactor, etc. For example, the x MHz RF generator, the y MHz RF generator, and the z MHz RF generator are coupled to an inductor within the ICP plasma chamber.
It is also noted that although the operations above are described as being performed by the processor 142 (
It should be noted that although the above-described embodiments relate to providing an RF signal to the lower electrode of the ESC 132 (
Embodiments described herein may be practiced with various computer system configurations including hand-held hardware units, microprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe computers and the like. The embodiments can also be practiced in distributed computing environments where tasks are performed by remote processing hardware units that are linked through a network.
With the above embodiments in mind, it should be understood that the embodiments can employ various computer-implemented operations involving data stored in computer systems. These operations are those requiring physical manipulation of physical quantities. Any of the operations described herein that form part of the embodiments are useful machine operations. The embodiments also relates to a hardware unit or an apparatus for performing these operations. The apparatus may be specially constructed for a special purpose computer. When defined as a special purpose computer, the computer can also perform other processing, program execution or routines that are not part of the special purpose, while still being capable of operating for the special purpose. In some embodiments, the operations may be processed by a general purpose computer selectively activated or configured by one or more computer programs stored in the computer memory, cache, or obtained over a network. When data is obtained over a network, the data may be processed by other computers on the network, e.g., a cloud of computing resources.
One or more embodiments can also be fabricated as computer-readable code on a non-transitory computer-readable medium. The non-transitory computer-readable medium is any data storage hardware unit that can store data, which can be thereafter be read by a computer system. Examples of the non-transitory computer-readable medium include hard drives, network attached storage (NAS), ROM, RAM, compact disc-ROMs (CD-ROMs), CD-recordables (CD-Rs), CD-rewritables (CD-RWs), magnetic tapes and other optical and non-optical data storage hardware units. The non-transitory computer-readable medium can include computer-readable tangible medium distributed over a network-coupled computer system so that the computer-readable code is stored and executed in a distributed fashion.
One or more features from any embodiment may be combined with one or more features of any other embodiment without departing from the scope described in various embodiments described in the present disclosure.
Although the foregoing embodiments have been described in some detail for purposes of clarity of understanding, it will be apparent that certain changes and modifications can be practiced within the scope of the appended claims. Accordingly, the present embodiments are to be considered as illustrative and not restrictive, and the embodiments are not to be limited to the details given herein, but may be modified within the scope and equivalents of the appended claims.
Howald, Arthur M., Valcore, Jr., John C.
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